Subgroups — D₁₉₆ #87625

Order 392.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₉	C₂²	1	1	yes	characteristic
4	D₄₉	—	2	2	no	—
5	D₂₈	—	7	1	no	maximal
6	C₄₉	D₄	1	1	yes	characteristic, complemented, Sylow
7	C₂×D₇	—	7	2	no	—
8	C₄×C₇	D₇	1	1	yes	characteristic
9	C₂×C₇	C₂×D₇	1	1	yes	characteristic
10	D₇	—	14	2	no	—
11	D₄	—	49	1	no	Sylow
12	C₇	D₂₈	1	1	yes	characteristic
13	C₂²	—	49	2	no	—
14	C₄	D₄₉	1	1	yes	characteristic, complemented
15	C₂	—	98	2	no	—
16	C₂	C₂×D₄₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.